State the domain where the function is analytic.

$\displaystyle f(z) = \frac{1}{1-z^4}$

From what I have studied, f(z) is analytic on a domain D, if f(z) is differentiable at all points in D.

However, I don't know where I should begin. And I think that $\displaystyle f(z)$ is not analytic at $\displaystyle 1-z^4=0$.

Anyway, how to find the domain, how to show in details to solve this.

Thank you.